Periodicity Search of Possible Counterparts to unidentified EGRET sources

Periodicity as a multiwavelength toolPeriodicity as a multiwavelength toolOutline :

Our method to perform periodicity search

Possible candidates of the next Geminga

Contribution of the archive data in our work

Periodicity as a Multiwavelength ToolPeriodicity as a Multiwavelength Tool

Variability studies have shown that pulsars have low variability (except for their pulsations), while blazars typically show more variability.

Periodic variability at multiple wavelengths is a definitive identifier.

Pulsars (rotating neutron stars) are the prototype of this approach.

The approach:

search out a periodic signal at one wavelength, then fold data from other wavelength bands at the expected period.

In addition to identification, periodic sources allow exploration of physical processes.

At some level, gamma-ray sources will have X-ray counterparts. If the X-ray counterpart can be found, the better X-ray position information allows deep searches at longer wavelengths. The classic example is Geminga. Bignami, Caraveo, Lamb, and Halpern started this search in 1983. The final result appeared in 1992 with the detection of pulsations from this isolated neutron star.

(Thompson, 2001)

J0218+4252

B1055-52Geminga

B0656+14

B1509-58

B1046-58B1706-44

Vela

B1951+32

Crab

T P / 2P= &

19B 3.2 10 PP× &:

463

PE 4 10P

= ×&&

38 1/ 2 3/ 2N 1.7 10 P P E−× ∝& & &:

20 3/ 2 1/ 2open 4 10 P P−Φ = × &

Characteristic age:

Spin-down energy:

Magnetic field:

Open field line voltage:

The current of relativistic particles flow:

year

erg/s

gauss

volt

s-1

Period v. Period derivative diagram for known Pulsars Period v. Period derivative diagram for known Pulsars

0.5-

2 K

eV2-

100

KeV

0.1-

10 M

eV>1

00 M

eV

Additional candidates:

>100 MeV

(Thompson, 2001)

Gamma-ray pulsars and Possible candidates:Gamma-ray pulsars and Possible candidates:

Gamma-ray pulsars :Gamma-ray pulsars :

Neutron starsNeutron starsNeutron Stars (~1400)

Isolated Neutron Stars In Binary systems

Radio-quiet INS Isolated Radio Pulsars

AXPs (~6)

RQINs without γ-rayRQINs with γ-ray

SGRs (~5)CCOs (~5)

XDINs (~7)

Others (>7)

Companion?

Radio emission ?

With γ-ray ?

With SNR ?

Possible Gamma-ray Pulsar CandidatesPossible Gamma-ray Pulsar CandidatesSurveying the Universe with EGRET 1991-1996

1st EGRET catalogue: 127 (1EG)2nd EGRET catalogue: 129 (2EG)Supplement to 2nd EGRET catalogue: 157 (2EGS)3th EGRET catalogue: 271 (3EG)

Oct, 2002

Unidentified EGRET sourcesUnidentified EGRET sourcesAccording to Lamb and Macomb, 1997; there are around 30 sources in the sky with GeV fluxes above 4x10-8 photons cm-2 s-1. Some of them which lie almost exclusively along the Galactic plane are currently unidentified.

From Roberts and Romani (2001), they present a catalog of 2-10 keV ASCA GIS images of fields containing bright sources of GeV emission. The images cover ~85% of the 95% confidence position contour for 28 of the 30 sources.

Among the unidentified sources of Robert’s catalog, we work on the periodicity search for 13 possible X-ray counterparts to gamma-ray pulsar candidates.

(Roberts ,Romani & Kawai ;2001)

X-ray archive data we usedX-ray archive data we usedRecent X-ray Missions:ROSAT(1990-1999) ASCA(1993-2001) RXTE(1995-)BeppoSAX(1996-2002) Chandra(1999-)XMM(1999-)

ROSATPSPC 0.1-2 keV ; 130 μsHRI 0.1-2.5 keV ; 61 μs

ASCAGIS 0.8-12 keV ; 62.5ms/2N; 500ms/2N

SIS 0.4-12 keV ;

BeepoSAXLECS 0.1-10 keV ; 16 μsMECS 1.3-10 keV ; 15 μs

ChandraACIS 0.2-10 keV ; 2.8 msHRC 0.1-10 keV ; 16 μs

XMM-NewtonMOS 0.1-15 keV ; 1.5 ms-2.6sPN 0.1-15 keV ; 7 μs-73.4 ms

--The archive data that we used--

Our method in periodicity searchOur method in periodicity searchThere are different methods to perform periodicity search, e.g., FFT, epoch folding, Zm

2-test, H-test, etc.

H-test:The H-test involves the Zm

2-static and Zm2 -Test as basis with chosen smoothing parameter (m=1,…,20)

The H-statistic is defined as

And the Zm2 -statistic is given by

here N is total number of detected photons, and φis the arrival phase of the ith photon where

ν is the trial frequency, t is the barycentic corrected arrival time of the photon, and t0 is time-zero epoch

The H-test offers some advantages over the other tests when searching for an unknown pulse shape in sparse data. It is independent of the binning of the data, and it is sensitive to a wide variety of pulse shapes.

H ≡

1≤m ≤20m ax Zm

2 −4m +4( )

Zm

2 ≡2N

[( cos2πkφii=1

N∑ )2 +( sin2πkφi

i=1

N∑ )2 ]

k=1

m∑

φ≡fractional πart of(n0(t−t0 )+

12&n0(t−t0 )

2 +12&&n0(t−t0 )

3)

The power of the H -test The power of the H -test

(De Jager,Swanepoel & Raubenheimer ;1989)

The power of the H -test The power of the H -test

(De Jager,Swanepoel & Raubenheimer ;1989)

According to the sensitivity of the sample size shown on the power of theH-test, I restricted the arbitrary condition that source photons > 100.

Unidentified Sources near radio pulsars I.Unidentified Sources near radio pulsars I.

Figure 1a. Results of periodicity search with the methodof H-test in the frequency range [14.66725,14.668] Hz which covers the estimated period of PSR J1420-6048.

Fig 1b. Pulse profile of ASCA data folded at 14.6676470 Hz. Total source counts are 252 and Fourier width is 5.78x10-6 Hz.

Observation Date(Mission)

Name of pulsar

Epoch ofephemeris

(MJD)

Estimated pulse frequency (Hz)

The maximum H value

of the trial

Random prob.

1999-02-13 (ASCA) J1420-6048 51223.68495 14.667647032(7) ~13.1 5.44x10-3

The pulse frequency of AX J1420.1-6049 can be inferred from PSR J1420-6048 (D’ Amico et al., 2001)

Unidentified Sources near radio pulsars II.Unidentified Sources near radio pulsars II.Observation Date

(Mission)Name of pulsar

Epoch ofephemeris

(MJD)

Estimated pulse frequency (Hz)

The maximum H value

of the trial

Random prob.

2001-10-18 (XMM) B1823-13 52200.36170 9.85473263939(5) ~14.4 3.24x10-3

Figure 2a. Results of periodicity search with the methodof H-test in the frequency range [9.851,9.86] Hz which covers the estimated period of PSR J1823-13.

Fig 2b. Pulse profile of XMM data folded at 8.854744 Hz. Total source counts are 1389 and Fourier width is 4.24x10-5 Hz.

The pulse frequency of *PSR B1823-13 can be infer from PSR B1823-13 (Gaensler et al., 2003)(Note: *PSR B1823-13 here implies the X-ray point source whose space position is consistent with the radio pulsar PSR B1823-13)

Observation Date(Mission)

Name of pulsar

Epoch ofephemeris

(MJD)

Estimated pulse frequency (Hz)

The maximum H value

of the trial

Random prob.

2003-02-12 (Chandra) J2021+3651 52682.60172 9.6409485566(1) ~21.0 2.34x10-4

Unidentified Sources near radio pulsars III.Unidentified Sources near radio pulsars III.

The pulse frequency of AX J2021.1+3651 can be inferred from PSR J2021+3651 (Roberts et al., 2002)

Figure 3a. Results of periodicity search with the methodof H-test in the frequency range [9.62,9.665] Hz which covers the estimated period of PSR J2021+3651.

Fig 3b. Pulse profile of Chandra data folded at 9.64094856 Hz. Total source counts are 575 and Fourier width is 4.81x10-

5 Hz..

Unidentified GeV sources which might be next GrmingaUnidentified GeV sources which might be next GrmingaThe only way is blind searchblind search and cross-checking cross-checking

Based on 4-7 independent significant trial periods which are selected by H-test from each X-ray data, we search related periods in other data of the same point source by the condition that the characteristic age of the pulsar is larger than 1000 years. Furthermore, in order to let our choice to be more convincible, we only consider that (The Random Probability to Corresponding H-value of Related Period) X (Number of Searching Trials under the Constraint of Characteristic Age) < 0.02.

To proof our method can be used to detect the weak pulsar candidates, we can examine our method in some CCOs and XDINs with their marginal evidence of the periodicity detection.

XDINS

CCO

(Pavlov, Sanwal & Garmire; 2001)

XMM-Newton Discovery of 7 s Pulsations in the INS XMM-Newton Discovery of 7 s Pulsations in the INS RX J1856.5-3754RX J1856.5-3754

Tiengo & Mereghetti (2007) reported the marginal period 7.055s of RX J1856.5-3754 by the periodicity search in XMM-Newton observation on 2006 Oct 24. Can we get any possible detection from the other archive data by usingour searching method?

Date Instrument Mode Exposure(ks) Epoch(MJD) Counts

2002 Apr 8 pnMOS2

SWSW

5758 52373.00618 328663

80202

2004 Apr 17 pn TI 65 53113.30249 276881

2004 Sep 24pn

MOS1MOS2

SWSWSW

337070

53272.479931852256491442733

2005 Sep 24pn

MOS1MOS2

SWSWSW

353535

53637.538651807703166235323

2006 Mar 26pn

MOS1MOS2

SWSWSW

707070

53821.058973789526866273664

2007 Mar 14 pn

MOS1MOS2

SWSWSW

666969

54174.236872825596110874751

Table. Log of XMM-Newton Observations of RX J1856.5-3754

Date The independent significant trial frequencypicked by blind search (Hz) H value Corresponding R.P.

with considering total trials

2002 Apr 8(52373.00618 MJD)

0.039832000.141745500.185506000.416623000.557842000.564043000.62697400

31.528.530.432.028.629.328.3

0.29870.60600.39530.26170.59390.51190.6301

2004 Apr 17(53113.30249 MJD)

0.025279000.032857000.037921000.075841000.380800000.62003800

33.034.733.236.439.333.3

0.22090.13830.2092

0.086040.038530.2035

2004 Sep 24(53272.47993 MJD)

0.057477500.107897500.628275000.660267500.94912250

26.226.526.326.432.8

0.91580.89170.90790.89990.2512

2005 Sep 24(53637.53865 MJD)

0.011280000.011425000.013160000.02354500

33.729.529.934.7

0.10350.33580.3020

0.07759

2006 Mar 26(53821.05897 MJD)

0.882424000.897266000.92011600

32.033.830.3

0.30550.18880.4643

2007 Mar 14 (54174.23687MJD)

0.010327500.070867500.14173400

37.336.436.6

0.070940.091120.08618

Table. The possible signal picked from each data by blind search

Results of Data Cross-CheckingResults of Data Cross-CheckingCompare to the periodicity data cross-checking in the X-ray counterparts of unidentified GeV sources, we show the possible pulsar candidates with the significance higher than 3.5 s (r.p. < 4.65x10-4) to eliminate the fake results induced by random noise at low frequencies.

RXJ1856.6-3754 period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 2.400252 XXX -0.74 52373.00618-54174.23687 1.84x10-4

P2 7.054898 26880 41.58 52373.00618-54174.23687 2.68x10-5

P3 7.054898 30390 36.78 52373.00618-54174.23687 2.31x10-5

P4 7.054898 43690 25.59 52373.00618-54174.23687 1.23x10-4

P5 7.054898 71820 15.56 52373.00618-53113.30249 3.92x10-4

P6 7.055470 21670 51.589 53113.30249-54174.23687 7.81x10-5

P7 7.055470 102920 10.86 53113.30249-54174.23687 3.89x10-4

P8 7.055470 20580 54.31 53272.47993-54174.23687 2.69x10-4

P9 7.055470 31810 35.14 53272.47993-54174.23687 7.28x10-5

P10 7.055470 4960 225.41 53637.53865-54174.23687 4.58x10-4

P11 7.055470 9920 112.71 53637.53865-54174.23687 1.57x10-4

P12 14.11084 20830 107.35 53637.53865-54174.23687 7.76x10-5

P13 25.1054 XXX -3628.66 52373.00618-53637.53865 6.67x10-5

P14 39.559 24480 256.09 53113.30249-54174.23687 7.59x10-5

Table. Possible pulsed candidates of RX J1856.5-3754

Results of Data Cross-CheckingResults of Data Cross-CheckingIf RX J1856.5-3754 is a normal pulsar without glitch, we can drop P1 & P13.From P2-P11, these pulsed candidates may attribute to the same period ~7.055s. And P12 might be induced by the half harmonic of the main pulsation.

The most significant case is P3 and reaches to 4s level.In our search, the spin period of RX J1856.5-3754 may range from 7.05490s to 7.05547s among 2002-2007, and This result is consistent with the pulsed period 7.055150.00007s reported by Tiengo & Mereghetti using the XMM observation on Oct. 24, 2006.

1.1x10−12ss−1 < &P< 2.3x10−11ss−1.

(−1.2x10−12ss−1 < &P<1.9x10−12ss−1(90% c.l.))

P3 is picked from 2 data cross-checking between [Apr. 8 ,2002] & [Mar. 14,2007]. To raise the significant level, we can check the pulsed strength in the otherdata. Date Trial frequency H value R.P.

2002 Apr 8 0.14174550 28.5 ----

2004 Apr 17 0.14174007 21.4 2.01x10-4

2004 Sep 24 0.14173976 24.8 5.62x10-5

2005 Sep 24 0.14173743 16.0 1.73x10-3

2006 Mar 26 0.14173625 14.4 3.29x10-3

2006 Oct 24 0.14173491 28.3 1.73x10-5

2007 Mar 14 0.14173400 36.6 ----

Compare with the pulsed profileCompare with the pulsed profileSimple Linear Regression

The minimization procedure forestimating parameters is calledmethod of least squares:

SSE = ei

2 = (yi −a−bx i)2

i=1

n

∑i=1

n

∑

Differentiating SSE with respect to a and b, we have

∂SSE∂a

=−2 (yi −a−bx i)=0i=1

n

∑

∂SSE∂b

=−2 (yi −a−bx i)x i =0i=1

n

∑ Solving 2 equations, we get:

b =n x iyi −( x i)( yi

i=1

n

∑i=1

n

∑ )i=1

n

∑

n x i2 − x i

i=1

n

∑⎛⎝⎜

⎞⎠⎟2

i=1

n

∑ a =y−bx & If we set 3 notations,

Sxx = (x i −x)

2 = x i2 −

x ii=1

n

∑⎛⎝⎜

⎞⎠⎟2

ni=1

n

∑i=1

n

∑ Syy = (yi −y)

2 = yi2 −

yii=1

n

∑⎛⎝⎜

⎞⎠⎟2

ni=1

n

∑i=1

n

∑;

Compare with the pulsed profileCompare with the pulsed profile

Syy = (x i −x)(yi −y)= x iyi −

( x i)( yi)i=1

n

∑i=1

n

∑ni=1

n

∑i=1

n

∑ ; thus b =

Sxy

Sxx

SSE = (yi −a−bx i)

2 = (yi −y)−b(x i −x)⎡⎣ ⎤⎦2

i=1

n

∑i=1

n

∑ =Syy−2bSxy+ b2Sxx =Syy−bSxy

0 < b2

Sxx

Syy

=1−SSESyy

<1

&

So,

To estimate the linear relationship between two variables x and y, we can

define Pearson r :

bSxx

Syy

=Sxy

SxxSyy

If we consider r2, then 100 • r2% of the variation in the values of y may be accountedfor by the linear relationship with the variable x. This relationship can be provedby the normal conditional distribution, and we can treat r2 as the proportion of thetotal variance that is explained from the prediction.

If we want to compare with 2 light curves, we can set the photon counts(after subtracting the average background photons) of each bin from thesame pulsed profile in one parameter (x or y). Then the correlation coefficientr will give us a basic information of the similarity.

Discovery of 424 ms Pulsations from the CCO Discovery of 424 ms Pulsations from the CCO 1E 1207.4-52091E 1207.4-5209

Zavlin & Pavlov et. al. (2000, 2002) reported the marginal pulsation 424ms of 1E 1207.4-5209 by the periodicity search in the Chandra observation on 2000 Jan 6 & 2002 Jan 5. (424ms~2.35777Hz)

Date The independent significant trial frequencypicked by blind search (Hz) H value Corresponding R.P.

with considering total trials

1992 Aug 2(48836.74673 MJD)

7.317484009.1318330053.389465059.631835066.357100095.2259800

40.842.641.741.942.243.5

0.88370.73440.81440.79740.77090.6491

1994 Jul 10(49543.21054 MJD)

26.244800058.458800061.616900064.5493000

34.933.233.637.3

0.32380.48050.43980.1758

1994 Jul 15(49548.60205 MJD)

1.311966004.407556004.456374005.96028200

39.253.738.840.6

0.44360.0004391

0.48100.3285

1994 Jul 18(49556.25311 MJD)

20.764888022.595329850.045934472.559985289.0471336

48.348.349.657.350.1

0.40710.40710.3197

0.00097560.01724

2000 Jan 17(51561.69778 MJD)

0.264586052.54485355.71751181.25580395.996820

46.544.843.648.146.4

0.82760.9363

<10.69650.8350

Table. The possible signal picked from each data by blind search

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

NR ICS

104 yr

106 yr

107 yr

Detected

CR

1011

G

1013

G 1014

G

1012

G

Radio-Loud Radio-Quiet

NR ICS

104 yr

106 yr

107 yr

1012

G

EGRET

CR

1011

G

1013

G10

14G

0.1 1 10Period (s)

NR ICS

1011

G

104 yr

106 yr

107 yr

1012

G

GLAST

CR

1013

G10

14G

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

0.1 1 10Period (s)

1014

G10

13G

NR ICS

1011

G

104 yr

106 yr

107 yr

CR

1012

G

AGILE

Bright g-ray pulsar Bright g-ray pulsar futurefuture

ConclusionConclusion

Obviously, applying for the better data is necessary to verify our results. To avoid a blind search with a huge number of trials, these candidate periods can serve as the target periods for future search when new data become available.

Period in the emission of other energy bands from the counterpart of the gamma-ray source may help to establish the periodicity in the gamma-ray emission and therefore strengthen the identification of the source in different energy bands.

We develop a procedure, by cross-checking at least two X-ray data sets, to find candidate periods for some specified sources.Our method can be examined in some CCO/XDIN data with marginal evidence for periodicity. We present our results of this method, which are part of our efforts to find the next radio-quiet gamma-ray pulsars.